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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.archetypes"></a><a class="link" href="archetypes.html" title="Conceptual Archetypes for Reals and Distributions">Conceptual Archetypes for Reals
    and Distributions</a>
</h2></div></div></div>
<p>
      There are a few concept archetypes available:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Real concept for floating-point types.
        </li>
<li class="listitem">
          Distribution concept for statistical distributions.
        </li>
</ul></div>
<h6>
<a name="math_toolkit.archetypes.h0"></a>
      <span class="phrase"><a name="math_toolkit.archetypes.real_concept"></a></span><a class="link" href="archetypes.html#math_toolkit.archetypes.real_concept">Real
      concept</a>
    </h6>
<p>
      <code class="computeroutput"><span class="identifier">std_real_concept</span></code> is an archetype
      for theReal types, including the built-in float, double, long double.
    </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">concepts</span><span class="special">/</span><span class="identifier">std_real_concept</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">concepts</span>
<span class="special">{</span>
  <span class="keyword">class</span> <span class="identifier">std_real_concept</span><span class="special">;</span>
<span class="special">}</span>
<span class="special">}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
      The main purpose in providing this type is to verify that standard library
      functions are found via a using declaration - bringing those functions into
      the current scope - and not just because they happen to be in global scope.
    </p>
<p>
      In order to ensure that a call to say <code class="computeroutput"><span class="identifier">pow</span></code>
      can be found either via argument dependent lookup, or failing that then in
      the std namespace: all calls to standard library functions are unqualified,
      with the std:: versions found via a <code class="computeroutput"><span class="keyword">using</span></code>
      declaration to make them visible in the current scope. Unfortunately it's all
      to easy to forget the <code class="computeroutput"><span class="keyword">using</span></code> declaration,
      and call the double version of the function that happens to be in the global
      scope by mistake.
    </p>
<p>
      For example if the code calls ::pow rather than std::pow, the code will cleanly
      compile, but truncation of long doubles to double will cause a significant
      loss of precision. In contrast a template instantiated with std_real_concept
      will <span class="bold"><strong>only</strong></span> compile if the all the standard
      library functions used have been brought into the current scope with a using
      declaration.
    </p>
<h3>
<a name="math_toolkit.archetypes.h1"></a>
      <span class="phrase"><a name="math_toolkit.archetypes.testing_the_real_concept"></a></span><a class="link" href="archetypes.html#math_toolkit.archetypes.testing_the_real_concept">Testing
      the real concept</a>
    </h3>
<p>
      There is a test program <a href="../../../test/std_real_concept_check.cpp" target="_top">libs/math/test/std_real_concept_check.cpp</a>
      that instantiates every template in this library with type <code class="computeroutput"><span class="identifier">std_real_concept</span></code>
      to verify its usage of standard library functions.
    </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">concepts</span><span class="special">/</span><span class="identifier">real_concept</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">concepts</span><span class="special">{</span>

<span class="keyword">class</span> <span class="identifier">real_concept</span><span class="special">;</span>

<span class="special">}}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
      <code class="computeroutput"><span class="identifier">real_concept</span></code> is an archetype
      for <a class="link" href="real_concepts.html" title="Conceptual Requirements for Real Number Types">user defined real types</a>,
      it declares its standard library functions in its own namespace: these will
      only be found if they are called unqualified allowing argument dependent lookup
      to locate them. In addition this type is useable at runtime: this allows code
      that would not otherwise be exercised by the built-in floating point types
      to be tested. There is no std::numeric_limits&lt;&gt; support for this type,
      since numeric_limits is not a conceptual requirement for <a class="link" href="real_concepts.html" title="Conceptual Requirements for Real Number Types">RealType</a>s.
    </p>
<p>
      NTL RR is an example of a type meeting the requirements that this type models,
      but note that use of a thin wrapper class is required: refer to <a class="link" href="high_precision/use_ntl.html" title="Using NTL Library">"Using
      With NTL - a High-Precision Floating-Point Library"</a>.
    </p>
<p>
      There is no specific test case for type <code class="computeroutput"><span class="identifier">real_concept</span></code>,
      instead, since this type is usable at runtime, each individual test case as
      well as testing <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span>
      <span class="keyword">double</span></code>, also tests <code class="computeroutput"><span class="identifier">real_concept</span></code>.
    </p>
<h3>
<a name="math_toolkit.archetypes.h2"></a>
      <span class="phrase"><a name="math_toolkit.archetypes.distribution_concept"></a></span><a class="link" href="archetypes.html#math_toolkit.archetypes.distribution_concept">Distribution
      Concept</a>
    </h3>
<p>
      Distribution Concept models statistical distributions.
    </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">concepts</span><span class="special">/</span><span class="identifier">distribution</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></pre>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
<span class="keyword">namespace</span> <span class="identifier">concepts</span>
<span class="special">{</span>
  <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">&gt;</span>
  <span class="keyword">class</span> <span class="identifier">distribution_archetype</span><span class="special">;</span>

  <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Distribution</span><span class="special">&gt;</span>
  <span class="keyword">struct</span> <span class="identifier">DistributionConcept</span><span class="special">;</span>

<span class="special">}}}</span> <span class="comment">// namespaces</span>
</pre>
<p>
      The class template <code class="computeroutput"><span class="identifier">distribution_archetype</span></code>
      is a model of the <a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">Distribution concept</a>.
    </p>
<p>
      The class template <code class="computeroutput"><span class="identifier">DistributionConcept</span></code>
      is a <a href="../../../../../libs/concept_check/index.html" target="_top">concept checking
      class</a> for distribution types.
    </p>
<h3>
<a name="math_toolkit.archetypes.h3"></a>
      <span class="phrase"><a name="math_toolkit.archetypes.testing_the_distribution_concept"></a></span><a class="link" href="archetypes.html#math_toolkit.archetypes.testing_the_distribution_concept">Testing
      the distribution concept</a>
    </h3>
<p>
      The test program <a href="../../../test/compile_test/distribution_concept_check.cpp" target="_top">distribution_concept_check.cpp</a>
      is responsible for using <code class="computeroutput"><span class="identifier">DistributionConcept</span></code>
      to verify that all the distributions in this library conform to the <a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">Distribution
      concept</a>.
    </p>
<p>
      The class template <code class="computeroutput"><span class="identifier">DistributionConcept</span></code>
      verifies the existence (but not proper function) of the non-member accessors
      required by the <a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">Distribution concept</a>.
      These are checked by calls like
    </p>
<pre class="programlisting"><span class="identifier">v</span> <span class="special">=</span> <span class="identifier">pdf</span><span class="special">(</span><span class="identifier">dist</span><span class="special">,</span> <span class="identifier">x</span><span class="special">);</span> <span class="comment">// (Result v is ignored).</span>
</pre>
<p>
      And in addition, those that accept two arguments do the right thing when the
      arguments are of different types (the result type is always the same as the
      distribution's value_type). (This is implemented by some additional forwarding-functions
      in derived_accessors.hpp, so that there is no need for any code changes. Likewise
      boilerplate versions of the hazard/chf/coefficient_of_variation functions are
      implemented in there too.)
    </p>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
      Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
      Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
      Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
      Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
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